Prof. Roman Slowinski(Poznan University of Technology, Laboratory of Intelligent Decision Support Systems, and Systems Research Institute, Polish Academy of Sciences, Poland)Interactive Robust Multiobjective Optimization Driven by Decision Rule Preference Model
Interactive procedures for multiobjective optimization (MOO) consist of a sequence of steps alternating calculation of a sample of non-dominated solutions and elicitation of preference information from the Decision Maker (DM). We consider three types of procedures, where in preference elicitation stage, the DM is just asked to indicate which solutions are relatively good in the proposed sample. In all three cases, the preference model is a set of decision rules inferred from the preference information using the Dominance-based Rough Set Approach (DRSA) [1,5]. The main advantage of decision rules is their simplicity and human-interpretable form. Moreover, they are able to model interactions between objectives. The first case is a deterministic MOO problem. Selected decision rules permit to focus progressively on the most interesting region of the Pareto-optimal set [2]. The second case is an optimization problem under uncertainty, exemplified by portfolio selection. Feasible portfolios are evaluated in terms of meaningful quantiles of the distribution of return. Using stochastic dominance on these quantiles, DRSA is producing decision rules guiding convergence to the most interesting region of the Pareto-optimal set [3]. The third optimization problem involves both multiple objectives and uncertainty. Some coefficients in the objective functions and/or constraints of this problem are not precisely known and given as interval values. The proposed interactive procedure is called DARWIN [4]. In the calculation stage, a sample of feasible solutions is generated together with a sample of vectors of possible values of the imprecise coefficients, called scenarios. Each feasible solution from the current sample is characterized by a distribution over generated scenarios. Some representative quantiles of these distributions are presented to the DM in the preference elicitation stage. The DM is indicating relatively good solutions and then DRSA based on first- or second-order stochastic dominance is producing decision rules exploited by an evolutionary search of a better sample of solutions.

Prof. Hiroyuki Tamura(Faculty of Engineering Science, Kansai University, Osaka, Japan)Modeling Ambiguity Averse Behavior of Individual Decision Making: Prospect Theory under Uncertainty
In this presentation, some behavioral (or descriptive) models of
individual decision making under risk and/or uncertainty are discussed.
Firstly, a behavioral model based on the "Prospect Theory" developed by
Kahneman and Tversky is described to explain the violations of expected
utility hypothesis. In this model outcome-dependent, non-additive
probabilities are introduced where probability of each event occurring is
known. The effective application of this approach to the public sector is
shown in modeling risks of extreme events with low probability and high
outcome. Next, a behavioral model based on our "Prospect Theory under
Uncertainty" is described where basic probability of a set of event is known
but occurrence probability of each event is not known. It is shown that this
model could properly explain the Elsberg paradox of ambiguity aversion.
Potential applicability of this approach to evaluating a global warming
problem is mentioned.

Prof. Weldon A. Lodwick(Department of Mathematical and Statistical
Sciences, University of Colorado, Denver, USA)The Relationship Between Fuzzy/Possibilistic Optimization and Interval Analysis
The relationship between fuzzy set theory (in particular fuzzy
arithmetic) and interval analysis is well-known. The interconnections
between interval analysis and fuzzy/possibilistic optimization via the
computation of the constraint set in the presence of possibilistic and fuzzy
uncertainty occurring in the set of constraint (in)equalities will be
developed. Moreover, the relationship of the united extension (the way to
compute functions of real-valued intervals) and Zadeh's extension principle
(the way to compute functions of real-valued fuzzy intervals) as it is
applied to optimization will be presented with special emphasis on
constraint fuzzy arithmetic and gradual numbers in the computation of
constraint sets and optimization algorithms. These ideas will be presented
within the context of an historical and taxonomic context.

Prof. Lluis Godo(IIIA - Artificial Intelligence Research Institute, CSIC - Spanish National Research Council, Bellaterra, Catalonia, Spain)g-BDI: a graded intensional agent model for practical reasoning
In intentional agents, actions are derived from the mental attitudes and
their relationships. In particular, preferences (positive desires) and
restrictions (negative desires) are important proactive attitudes which
guide agents to intentions and eventually to actions. In this talk we will
present joint work with Ana Casali and Carles Sierra about a multi-context
based agent architecture g-BDI to represent and reasoning about gradual
notions of desires and intentions, including sound and complete logical
formalizations. We also show that the framework is expressive enough to
describe how desires, together with other information, can lead agents to
intentions and finally to actions. As a case-study, we will also describe
the design and implementation of recommender system on tourism as well as
the results of some experiments concerning the flexibility and performance
of the g-BDI model.

Prof. Sadaaki Miyamoto(Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba, Ibaraki, Japan)Generalized bags, bag relations, and applications to data analysis and
decision making
Bags alias multisets are old in computer science but recently more
attention is paid on bags.
In this paper we consider generalized bags which include real-valued bags,
fuzzy bags, and fuzzy number-valued bags.
Basic definitions as well as their properties are established; advanced
operations such as t-norms, conorms, and their duality are also studied.
Moreover bag relations are discussed which has max-plus and max-min
algebras as special cases.
The reason why generalized bags are useful in applications is described. As
two application examples,
bag-based data analysis and decision making based on convex function
optimization related to bags are discussed.